Apple handles a variety of user data. Different types of data are stored and protected in different ways, at times for reasons beyond Apple's control. Some of that data (for example email) has very little protection because the underlying technology is inherently not secure. To demand that Apple make email secure would be like demanding that the Post Office figure out how to make post cards secure. It's impossible because it was never designed to be secure. There's not much Apple can do about that other than encourage its users to use better and more secure technologies instead.
If I understand correctly, anything stored in the cloud using your Apple ID login could be accessed by Apple (iCloud Photo Library, for example?). So Apple could be ordered by a court to make this data available to law enforcement on a case by case basis. But Apple, unlike some other companies, will not provide access to this type of data just for the asking, without a court order.
Then there's data that may be stored only on your device, like an iPhone (for example photos, if you have cloud photo services disabled, and also Messages data). Apple have made secure encryption standard on iOS devices for quite some time now and, depending on your settings and the quality of your password, it may be impossible for even Apple to access this data - which was Apple's intention. The DOJ wants Apple to eliminate this option and to ensure everything stored on its devices is accessible to law enforcement, which Apple is unwilling to do for what should be obvious reasons.